Multi-soliton solutions for the coupled modified nonlinear Schrödinger equations via Riemann–Hilbert approach**Project supported by the National Natural Science Foundation of China (Grant Nos. 61072147 and 11271008).

Abstract

The coupled modified nonlinear Schrödinger equations are under investigation in this work. Starting from analyzing the spectral problem of the Lax pair, a Riemann–Hilbert problem for the coupled modified nonlinear Schrödinger equations is formulated. And then, through solving the obtained Riemann–Hilbert problem under the conditions of irregularity and reflectionless case, N-soliton solutions for the equations are presented. Furthermore, the localized structures and dynamic behaviors of the one-soliton solution are shown graphically.